Simultaneous modeling of habitat suitability ... - ESA Journals

Ecological Applications, 20(4), 2010, pp. 1173–1182 Ó 2010 by the Ecological Society of America

Simultaneous modeling of habitat suitability, occupancy, and relative abundance: African elephants in Zimbabwe JULIEN MARTIN,1,2,7 SIMON CHAMAILLE´-JAMMES,3 JAMES D. NICHOLS,2 HERVE´ FRITZ,3 JAMES E. HINES,2 CHRISTOPHER J. FONNESBECK,4 DARRYL I. MACKENZIE,5 AND LARISSA L. BAILEY6 1

2

Florida Cooperative Fish and Wildlife Research Unit, University of Florida, Gainesville, Florida 32611-0485 USA Patuxent Wildlife Research Center, United States Geological Survey, 12100 Beech Forest Road, Laurel, Maryland 20708 USA 3 Universite´ de Lyon, Universite´ Lyon 1, CNRS, UMR 5558, Laboratoire de Biome´trie et Biologie Evolutive, 43 Boulevard du 11 Novembre 1918, Villeurbanne F-69622 France 4 Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand 5 Proteus Wildlife Research Consultants, P.O. Box 5193, Dunedin, New Zealand 6 Department of Fish, Wildlife and Conservation Biology, 1474 Campus Delivery, Fort Collins, Colorado 80523 USA

Abstract. The recent development of statistical models such as dynamic site occupancy models provides the opportunity to address fairly complex management and conservation problems with relatively simple models. However, surprisingly few empirical studies have simultaneously modeled habitat suitability and occupancy status of organisms over large landscapes for management purposes. Joint modeling of these components is particularly important in the context of management of wild populations, as it provides a more coherent framework to investigate the population dynamics of organisms in space and time for the application of management decision tools. We applied such an approach to the study of water hole use by African elephants in Hwange National Park, Zimbabwe. Here we show how such methodology may be implemented and derive estimates of annual transition probabilities among three dry-season states for water holes: (1) unsuitable state (dry water holes with no elephants); (2) suitable state (water hole with water) with low abundance of elephants; and (3) suitable state with high abundance of elephants. We found that annual rainfall and the number of neighboring water holes influenced the transition probabilities among these three states. Because of an increase in elephant densities in the park during the study period, we also found that transition probabilities from low abundance to high abundance states increased over time. The application of the joint habitat–occupancy models provides a coherent framework to examine how habitat suitability and factors that affect habitat suitability influence the distribution and abundance of organisms. We discuss how these simple models can further be used to apply structured decision-making tools in order to derive decisions that are optimal relative to specified management objectives. The modeling framework presented in this paper should be applicable to a wide range of existing data sets and should help to address important ecological, conservation, and management problems that deal with occupancy, relative abundance, and habitat suitability. Key words: adaptive resource management; African elephants; detection probabilities; Hwange National Park, Zimbabwe; joint habitat occupancy modeling; Loxodonta africana; multistate site occupancy models; structured decision making; surface water.

INTRODUCTION Conservation of natural resources often requires managing abundance and spatial distribution of organisms by acting on their habitat (Williams et al. 2002, MacKenzie et al. 2006). One challenge is then to capture the features of the system that are most relevant to the management objectives while keeping the models as simple as possible (Clark and Mangel 2001, Nichols Manuscript received 19 February 2009; revised 27 July 2009; accepted 5 August 2009. Corresponding Editor: J. J. Millspaugh. 7 Present address: Fish and Wildlife Research Institute, 100 8th Avenue SE, St. Petersburg, Florida 33701 USA. E-mail: julienm@ufl.edu

2001). The ability to simplify a problem to its most critical components (i.e., develop a model) has often been viewed as an art essential to the advancement of science (Clark and Mangel 2001). In the context of management there are at least two additional arguments in favor of using simple models: (1) logistical difficulty of accumulating detailed information over large spatiotemporal scales; (2) computational limitations associated with structured decision-making tools for deriving decisions that are optimal relative to management objectives (Conroy and Moore 2001). The recent development of statistical models such as dynamic site occupancy models provides the opportunity to resolve fairly complex management and conservation problems with relatively simple models (MacKenzie et al. 2006, 2009).

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Surprisingly few empirical studies have modeled simultaneously the dynamics of habitat suitability, occupancy, and abundances of organisms. Nevertheless, many ecologists have recognized the importance of modeling simultaneously occupancy and habitat suitability in the context of metapopulation dynamics (Lande 1987, Ovaskainen and Hanski 2003, MacKenzie et al. 2006). In this way, the status of a species can be evaluated based not only on occupancy, but also on suitability, of the potential habitats (Lande 1987, Ovaskainen and Hanski 2003, MacKenzie et al. 2006). Joint modeling of these components is therefore particularly important in the context of management of populations (where management may involve habitat modifications or manipulations), as it provides a coherent framework for investigating the population dynamics of organisms in space and time for the application of management decision tools (MacKenzie et al. 2006). Here we show how such an approach may be implemented and provide an example combining simultaneous modeling of habitat suitability and occupancy states (i.e., low and high abundances) in the context of the management of the population of African elephants (Loxodonta africana) (Blumenbach) of Hwange National Park, Zimbabwe. Densities of African elephants have increased significantly in southern Africa, reaching very high densities in some protected areas (Blanc et al. 2007). In such places, concerns emerge that high elephant abundance may be detrimental to biodiversity, particularly through the impact of elephants on vegetation (O’Connor et al. 2007). Culling has been proposed as a possible management action, but this option is ethically debatable and remains politically unattractive to many park managers and other stakeholders (Owen-Smith et al. 2006). Studies conducted in Hwange National Park suggest that managing surface water may offer an alternative, more appealing, management strategy in some places (Owen-Smith et al. 2006, Chamaille´Jammes et al. 2007b, c, Smit et al. 2007). By acting on the number and distribution of suitable water holes (i.e., retaining water during the dry season) through changes in artificial water supply, managers may be able to influence the abundance and distribution of elephants within parks. This, however, requires developing an understanding of the dynamics of elephant distribution across water holes. We had two primary objectives related to conservation and management of elephants. Our first objective was to better understand factors that govern site occupancy dynamics of elephants in Hwange National Park. Our second objective was to provide estimates of transition probabilities to parameterize mechanistic models that can be used as the basis for management purposes (e.g., to identify decisions that are optimal relative to specified management objectives; or to simulate abundance and distribution of elephants under a variety of management scenarios). Our models were based on several a priori hypotheses and predictions.

Ecological Applications Vol. 20, No. 4

We used likelihood-based dynamic multistate site occupancy models (MacKenzie et al. 2009) to estimate annual transition probabilities among three dry-season states (m) of sites: unsuitable sites (denoted U, hence m ¼ U), suitable sites with low abundance of elephants (0–50 counted over 24-h surveys, m ¼ L), and suitable sites with high abundance of elephants (51–1600, m ¼ H). In the context of our study, the sites were water holes. Water holes were considered suitable habitats whenever at least some water was present, and were considered unsuitable otherwise. For our purposes, we used the conditional binomial parameterization of the dynamic multistate model, ½m ½m wtþ1 Rtþ1 (as denoted by MacKenzie et al. 2009), where ½m wtþ1 is the probability that a water hole is suitable in year t þ 1 (i.e., contains water), given that the water hole was in state m in year t (with m being state U, L, or H); ½m and Rtþ1 is the probability that a suitable water hole contains a high abundance of elephants (state H) in year t þ 1, given that it was in state m in year t. For example, ½U wtþ1 is the probability of a water hole being suitable in year t þ 1, given that the water hole was unsuitable in year t (i.e., was in state U). The parameterization just ½m ½m described (hereafter referred to as wtþ1 Rtþ1 , or the conditional binomial parameterization) provides a natural description of the process we are trying to model. Indeed, water holes are suitable or not (described ½m by parameter wtþ1 ), and if they are suitable they are occupied either by a low or high number of elephants ½m (described by parameter Rtþ1 ). In order to evaluate the effect of several covariates (e.g., precipitation) on ½m ½m transition probabilities wtþ1 and Rtþ1 , we developed models that explicitly included these factors. For each of the hypotheses, we made specific predictions about the ½m influence of our selected covariates on parameters wtþ1 ½m and Rtþ1 . First, we evaluated the hypothesis that rainfall influences habitat suitability. Because the probability that water holes retain water increases with increasing rainfall (Chamaille´-Jammes et al. 2007a), we predicted a positive relationship between rainfall and the probability of transitioning from any state m at time t to a suitable ½m state at time t þ 1 (i.e., wtþ1 ). Our primary interest was to obtain reliable estimates of the magnitude of the rainfall effect on habitat (water hole) transition probabilities. Because this information may ultimately be incorporated into models that project the dynamics of elephants at water holes, it was necessary for us to evaluate this prediction, even though it may appear rather simple and obvious. Second, we evaluated the hypothesis that the total number of water holes within a 10 km radius of a focal water hole would influence the number of elephants present at that water hole site. We chose 10 km because most family herds typically do not travel .10 km from water during the peak of the dry season (Stokke and du Toit 2002). More specifically, we predicted a positive relationship between the number of neighboring water

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holes associated with a site and the probability that a site would transition to a high elephant abundance state at time t þ 1, given that the site was suitable in t þ 1 (i.e., ½m Rtþ1 is influenced by the number of neighboring water holes). Elephants may select sites with higher densities of water holes to reduce their chance of being located far away from any suitable sites if one or more neighboring sites become unsuitable. Finally, we considered the potential influence, of a general increase in elephant abundance in the park on site-specific elephant abundance transition probabilities ½m Rtþ1 . Regular culling of elephants was conducted in Hwange National Park until 1986. To avoid the disturbing effects of culling on elephant distribution we used data collected afterward, when the population first increased dramatically and then fluctuated at higher abundance (Chamaille´-Jammes et al. 2008). Thus, we ½m predicted that transition probabilities Rtþ1 have increased during the second half of the study period (1996–2005). METHODS Study area Hwange National Park covers ;15 000 km2 at the northwest border of Zimbabwe (19800 0 S, 26830 0 E). Vegetation is typical of southern African dystrophic wooded savannas with patches of grassland. Surface water becomes scarce during the dry season, as the river network and most natural pans dry up. In addition to the few natural water holes retaining water throughout the dry season, artificial water holes can maintain water availability year-round through ground water pumping (Fig. 1). Due to increased surface water availability, the elephant population has increased since the creation of the park and has been controlled through culling up to 1986. The population has increased dramatically since then and appears to have stabilized at .2 elephants/km2 (Chamaille´-Jammes et al. 2008). Heterogeneity across space in elephant densities during the dry season is linked to surface water availability (Chamaille´-Jammes et al. 2007a). Surveys We used survey data that were collected between 1987 and 2005, after culling operations were stopped. Water holes were surveyed annually during the dry season (between September and October). Over a 24-h period at full moon, all animals coming to drink were simultaneously recorded at the studied water holes from observation platforms or cars located close to the water hole (see Plate 1). Analyses of these census data in the context of elephant management can be found in Chamaille´-Jammes et al. (2007a, 2008) and Valeix et al. (2008). Statistical analysis We used likelihood-based dynamic multistate site occupancy models (MacKenzie et al. 2009) to estimate

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FIG. 1. Map of the study area, which encompasses the entire Hwange National Park, Zimbabwe. Open squares indicate the unmanaged water holes that were included in the statistical analyses. Open circles indicate the unmanaged water holes that were not included in the analyses. Solid circles indicate the sites that could possibly be equipped with water pumps.

½m

½m

annual transition probabilities (wtþ1 and Rtþ1 , described earlier), the probability that a water hole was suitable at time t (wt), and the probability that a water hole had a high abundance of elephants at time t, given that the water hole was suitable at time t (Rt). We followed the notation of MacKenzie et al. (2009), according to which ½m ½m transition probabilities (wtþ1 and Rtþ1 ) carry a superscript, whereas state variables (wt and Rt) do not. As explained earlier, sites could be in one of three states (m): unsuitable sites (denoted U, hence m ¼ U; i.e., water holes with no water); suitable sites (i.e., water holes with some water) with low abundance of elephants (0 to 50, m ¼ L), and suitable sites with high abundance of elephants (51–1600, m ¼ H). Initially we considered models that included more states; unfortunately, sample sizes were too small to produce reliable estimates and we had to limit our analysis to the three states just described. Beyond the obvious distinction between unsuitable and suitable sites, the cutoff point between low and high abundance had to distinguish an abundance category for which the impact of elephants at the water hole was deemed acceptable to park managers from a category for which impact may be too high. There are few data in the literature to link elephant impact to elephant numbers, and we based our cutoff point on the observation that at water holes where elephant abundance was lower than 50, neighboring vegetation did not suffer significant damage (S. Chamaille´-Jammes and H. Fritz, personal observation). Thus, we believe that the three states make sense from a management standpoint. An additional benefit of using only three states is related to computational limitations associated with decision-

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making tools (e.g., stochastic dynamic programming) for deriving optimal decisions with respect to specified management objectives (Conroy and Moore 2001). Although elephant census data were collected at 110 water holes, we only used natural water holes that were not equipped with pumps, reducing our sample size to 47 sites. We focused on natural water holes because for the other sites there was no good record of when pumps were active or not. This uncertainty made it impossible to separate influences of rain from those of pumping for sites with pumps. The count of the number of neighboring water holes (used as a covariate) included all water holes (i.e., those with and without pumps, as well ones for which count data were not available; this total number was 163 water holes). In our model notation, time dependency was denoted as ‘‘t,’’ and no time variation was denoted ‘‘.’’. For instance, fw[m](t)g indicates the habitat transition ½m probabilities, wtþ1 , varied over time, whereas fw[m](.)g, m remained constant over time. We also indicates that w½tþ1 developed several models that included the effect of ½m ½m factors of particular interest on wtþ1 and Rtþ1 : annual rainfall (denoted RAIN) and the number of neighboring water holes within a 10 km radius of each water hole site (denoted NEI). Annual rainfall for year t was computed as the cumulative rainfall from October in year t 1 to September in year t (Chamaille´-Jammes et al. 2007a). Annual rainfall for the period 1987–2005 ranged from 289 mm to 850 mm. Finally, we considered models that incorporated the increase in elephant abundance in the park. In order to account for this effect, we considered a ‘‘before vs. after effect 1996’’ (denoted BA; the ‘‘before’’ time period corresponded to the first half of the study period, 1987–1996). With these models, we predicted that transition probabilities toward high-abundance states would increase during the second half of the study period, due to the global population increase over the study period. By dividing the study period into two periods of ;10 years each, we were able to compute estimates that were relatively precise, yet reflected this ½m change in abundance. Note that we only modeled Rtþ1 as a function of NEI and BA. Although we had a priori ½m reasons to model wtþ1 as a function of rainfall (i.e., the probability of a site being suitable depends on rainfall), we did not have a priori reasons to believe that the number of neighboring water holes or the study period (BA effect) had an effect on water hole suitability (i.e., ½m w1, wtþ1 ). In contrast, we had a priori reasons to expect that transition probabilities to suitable states L or H ½m (indicated by Rt ) depended on NEI and BA. To illustrate how our a priori expectations are integrated into the models, we present the following example. Model fw[m](RAIN)R[m](RAIN þ NEI þ BA)g ½H U L , w½tþ1 , and wtþ1 were all assumed that transitions w½tþ1 affected by rainfall. The second term in the model ½U ½L ½H indicates that Rtþ1 , Rtþ1 , and Rtþ1 were influenced by rainfall, the number of neighboring water holes and a ‘‘before vs. after 1996’’ effect. No interactions among

these three predictor variables were considered; hence, the effect of the variables are additive (on the logistic scale) as denoted by the ‘‘þ’’ symbol. All models were fitted in program PRESENCE 2.2 (Hines 2008). Although the models and software that we used can estimate detection probabilities, in our application the ‘‘robust design survey data’’ (i.e., repeat surveys within each year over several years; for details, see MacKenzie et al. 2006) necessary to estimate detection were not available. However, elephants in non-forested habitat provide a sampling situation in which detection probabilities are expected to be extremely high. In the context of this application, ‘‘perfect detection’’ equates to correctly identifying water holes as having either low or high elephant abundance. Given the abundance categories used here, we believe this assumption is reasonable and therefore we fixed detection probability parameters to 1 in program PRESENCE 2.2 (Hines 2008). We also could have used an alternative formulation to directly model transition probabilities among states (U, ½m ½m L, and H) instead of using the wtþ1 Rtþ1 conditional binomial parameterization. In a typical multistate model, /½tqs can be defined as the probability that a site in state q at time t is in state s at time t þ 1. In this example, q and s are states (i.e., L, H, or U defined ½UH earlier). For instance, /t is the probability that a site that is unsuitable (i.e., in state U) at time t is suitable and is occupied by more than 50 elephants (i.e., is in state H) at time t þ 1. As explained by MacKenzie et al. (2009), there is a straightforward correspondence between these two parameterizations: 2 3 ½U ½L ½H 1 wtþ1 1 wtþ1 1 wtþ1 6 ½U U ½L ½L ½H ½H 7 4 wtþ1 ð1 R½tþ1 Þ wtþ1 ð1 Rtþ1 Þ wtþ1 ð1 Rtþ1 Þ 5 ½U

½U

½L

wtþ1 Rtþ1 2

/UU 6 tUL ¼ 4 /t /UH t

½L

wtþ1 Rtþ1 /LU t /LL t /LH t

½H

½H

wtþ1 Rtþ1

3 /HU t 7 /HL t 5: HH /t ð1Þ ½qs

Therefore, one can derive estimates for the /t parameterization from estimates obtained from the ½m ½m wtþ1 Rtþ1 parameterization. One advantage of using the latter parameterization is that both parameters are modeled as binomial random variables. Thus, one does not have to constrain the transition probabilities out of a ½m ½m particular state to sum to 1, making the wtþ1 Rtþ1 parameterization more stable computationally. In addition, with our covariate modeling, it was natural to ½m focus separately on habitat transitions (wtþ1 ) and elephant abundance transitions conditional on habitat ½m suitability (Rtþ1 ). Therefore, we first estimated parame½m ½m ters wtþ1 and Rtþ1 and then, to gain complementary insights, we used these estimates to derive unconditional

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transition probability (/t ) estimates among states U, L, and H. Regardless of the parameterization, a typical encounter history at water hole j (noted hj) would look like: hj ¼ HLUL; that is, the site contained water and over 50 elephants (state H) during the first season, it contained water but ,50 elephants were counted (state L) during the second and fourth seasons and the site was dry (state U) in the third season. The probability statement for this encounter history under model fw[m](t)R[m](t)g based ½m ½m on the wtþ1 and Rtþ1 parameterization would be: ½H ½H ½L ½U ½U w1R1w2 (1 R2 )(1 w3 )w4 (1 R4 ). The statement w1R1 corresponds to the probability of the water hole being suitable and being in state H during the first ½H ½H occasion. The terms w2 (1 R2 ) correspond to the probability of the water hole remaining suitable but moving to state L between time periods 1 and 2. ½L Similarly, (1 w3 ) corresponds to the probability that a site in state L at time 2 transitions to unsuitable in time ½U ½U 3. Finally, the terms w4 (1 R4 ) reflect the probability of the site becoming suitable between times 3 and 4 and then being characterized by a low abundance of elephants at time 4. We used Akaike’s information criterion (AIC) for model selection (Akaike 1973, Burnham and Anderson 2002). DAIC for the ith model was computed as AICi minimum AIC. AIC weight (w) was also used as a measure of relative support for each model (w ranged from 0 to 1, with 1 indicating maximum support; Burnham and Anderson 2002). Effect of covariates on transition probabilities ½m

½m

Parameters wtþ1 and Rtþ1 were modeled as a linearlogistic function of rainfall (RAIN), the number of neighboring water holes (NEI), and the ‘‘before vs. after 1996’’ effect (BA). ½m For example, Rtþ1 was modeled as ! ½m Rtþ1 ½m logit Rtþ1 ¼ ln ½m 1 Rtþ1 ¼ bINT þ bRAIN 3ðRAINÞ þ bBA 3 BA ð2Þ where bINT is the intercept and bRAIN is the slope m . parameter for the relationship between rainfall and R½tþ1 Although rainfall was measured in millimeters, it was converted to meters in the analysis; hence bRAIN should be interpreted in terms of meters of rainfall. bBA is the parameter that accounts for the ‘‘before vs. after 1996’’ effect. BA ¼ 1 corresponds to the first half of the study period (1987–1996) and BA ¼ 0 corresponds to the second half of the study period (1997–2005). RESULTS AIC model weights (w) suggested that the model fw[m](RAIN)R[m](RAIN þ NEI þ BA)g was best supported by the data (w ¼ 0.93; Table 1). As expected, the model revealed a positive relationship between

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TABLE 1. Model selection of joint habitat occupancy models for elephants in Hwange National Park, Zimbabwe. Model [m]

w w[m] w[m] w[m] w[m] w[m] w[m] w[m] w[m]

[m]

(RAIN) R (RAIN þ NEI þ BA) (RAIN) R[m] (RAIN þ BA) (RAIN) R[m] (RAIN þ NEI) (RAIN) R[m] (RAIN) (RAIN) R[m] (BA) (RAIN) R[m] (.) (.) R[m] (RAIN þ NEI þ BA) (.) R[m] (NEI) (.) R[m] (.)

DAIC

w

K

0 5.6 9.2 10.9 21.4 27.1 37.5 62.1 63.9

0.93 0.06 0.01 0 0 0 0 0 0

20 17 17 14 14 11 17 11 8

Notes: The parameter w[m] corresponds to the component of ½m the model that pertains to transition probability wtþ1 , the probability that a water hole is suitable in year t þ 1, given that the water hole was in state m in year t (with m being state: unsuitable [U], low abundance [L], or high abundance [H]). R[m] corresponds to the component of the model that pertains to trans½m ition probability Rtþ1 ; the probability that a suitable water hole contains a high abundance of elephants (state H) in year t þ 1, given that it was in state m in year t. BA is the before–after effect; NEI is the number of neighboring water holes; RAIN is rainfall at time t. AIC is the Akaike information criterion; DAIC for the ith model is computed as AICi minimum AIC; w is the AIC weight; K is the number of parameters.

rainfall (RAIN) and the probability that a water hole m was suitable, w½tþ1 , regardless of the occupancy state at time t (Table 2, Fig. 2). The number of neighboring water holes (NEI) was also included in the most parsimonious model, indicating that this factor influences the distribution of elephants at the water holes, ½m Rtþ1 . However, the predicted positive relationship between the number of neighboring water holes and ½m Rtþ1 was equivocal. For instance, the data suggested a ½H ½L ½U positive relationship for Rtþ1 , but not for Rtþ1 and Rtþ1 (Table 2, Fig. 3). There was some evidence that transition probabilities from any state at time t to high abundance at time t þ 1, given that the water hole was m ), were greater during the suitable at time t þ 1 (R½tþ1 second half of the study period (Fig. 3). Indeed, ½m estimates of Rtþ1 were greater during the second half of the study period than during the first half (i.e., bˆ BA ½U ½L ½H was negative for Rtþ1 , Rtþ1 , and Rtþ1 ; BA ¼ 1 corresponds to the first time period, 1987–1996; see Table 2). However, the confidence intervals for the estimated slope parameters overlapped zero for all ½H transition probabilities except Rtþ1 . There was negative ½U ½L relationship between annual rainfall and Rtþ1 , Rtþ1 , and ½H Rtþ1 , which would indicate that as precipitation increases, elephants tend to disperse (bˆ RAIN was negative for each of these parameters; Table 2). Using Eq. 1 and the estimates presented in Table 2, we derived estimates of /½tLH and /½tHL as a function of the number of neighboring water holes, precipitation, and the ‘‘before vs. after 1996’’ effect (Fig. 4). There was ½LH some evidence that /t decreased during years of high precipitation, but there was no evidence of a relationship between the number of neighboring water holes and ½LH (Fig. 4a). Conversely /½tHL increased during years /t

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TABLE 2. Parameter estimates for the most parsimonious model, with standard errors and upper and lower 95% confidence limits. w[m](RAIN) R[m](RAIN þ NEI þ BA)

b

Estimate

SE

Lower 95% CI

Upper 95% CI

¼ bINT þ bRAIN 3 RAIN

bINT bRAIN

4.667 5.773

0.688 1.056

6.042 3.660

3.292 7.885

logit(wtþ1 ) ¼ bINT þ bRAIN 3 RAIN

½L

bINT bRAIN

1.257 3.282

1.347 2.455

3.950 1.627

1.436 8.192

½H

bINT bRAIN

0.197 2.612

0.707 1.344

1.611 0.076

1.217 5.300

½U

bINT bRAIN bNEI bBA

8.199 8.525 0.371 1.439

2.978 3.363 0.147 0.872

2.243 15.252 0.666 3.184

14.154 1.799 0.076 0.306

½L

bINT bRAIN bNEI bBA

3.548 4.996 0.007 0.660

2.000 3.288 0.140 0.877

0.451 11.571 0.273 2.414

7.547 1.580 0.287 1.095

½H

bINT bRAIN bNEI bBA

4.446 5.953 0.233 1.817

1.486 2.077 0.111 0.733

1.474 10.107 0.011 3.283

7.417 1.799 0.456 0.350

½U logit(wtþ1 )

logit(wtþ1 ) ¼ bINT þ bRAIN 3 RAIN logit(Rtþ1 ) ¼ bINT þ bRAIN 3 RAIN þ bNEI 3 NEI þ bBA 3 BA

logit(Rtþ1 Þ ¼ biNT þ bRAIN 3 RAIN þ bNEI 3 NEI þ bBA 3 BA

logit(Rtþ1 ) ¼ bINT þ bRAIN 3 RAIN þ bNEI 3 NEI þ bBA 3 BA

Notes: BA is the before–after effect (BA ¼ 1 corresponds to the first half of the study period [1987–1996]; BA ¼ 0 corresponds to the second half of the study period [1997–2005]). NEI is the number of neighboring water holes; RAIN is rainfall at time t; bINT is m ; bBA is the parameter that accounts for the intercept, and bRAIN is the slope parameter for the relationship between rainfall and R½tþ1 the ‘‘before vs. after 1996’’ effect; and bNEI is the slope parameter for the relationship between the number of neighboring water ½m holes and Rtþ1 .

of high precipitation and there was some evidence of a negative relationship between the number of neighbor½HL ½LH ing water holes and /t (Fig. 4b). In addition, /t was greater during the second half of the study period, ½HL whereas the opposite was observed for /t (Fig. 4). Based on the most parsimonious model, the estimate of the probability of a water hole being suitable in 1987, wˆ 87, was 0.31 (SE ¼ 0.08) and the probability that a suitable water hole contained a high abundance of elephants (state H) in 1987, given that it was suitable in 1987, Rˆ 87, was 0.78 (SE ¼ 0.14). The remaining models received very little support from the data, based on w (w 0.06; Table 1). Model w[m](t)R[m](t) did not reach numerical convergence and therefore was not included in our evaluation of competing models. DISCUSSION Despite the importance of modeling occupancy and habitat suitability simultaneously, examples of such studies are scarce (Lande 1987, Ovaskainen and Hanski 2003, MacKenzie et al. 2006). Here we have modeled the habitat at a site as either unsuitable (i.e., with no water and therefore no chance of any elephants being present) or suitable. Suitable sites are then further categorized into one of two possible states. In our case, the occupancy states were two classes of abundance (low or high), although in other applications other categories could be used (e.g., presence or absence of the target species). In fact, a greater number of categories could be used if conducive with the objective of the study and if adequate data are available. Here we have also assumed that these categories are observed without error, but the modeling framework presented by MacKenzie et al.

(2009) is flexible enough to relax this assumption. This modeling framework is implemented in easy-to-use software PRESENCE 2.2, which should make this approach all the more useful to ecologists, conservation biologists, and managers. The results regarding our specific case study provide useful insights into the dynamics of elephants at water holes, which can be used to better manage elephant populations in Hwange National Park. As expected from previous studies of this system (Chamaille´-Jammes et al. 2007a, 2008), rainfall appears to be critical in influencing the distribution and abundance of elephants in the park (Fig. 2, Table 2). All supported models suggest a strong positive relationship between rainfall and the transition probabilities from unsuitable to suitable states. As explained earlier, our goal was not so much to further test the hypothesis that rainfall influences water hole suitability (which is self evident and was shown by Chamaille´-Jammes et al. 2007a), but rather to estimate parameters of this relationship for the purpose of modeling the effect of rainfall on water hole suitability (Fig. 2). Models that included the effects of the number of neighboring water holes (within 10 km) received some support. However, support for the prediction of a positive relationship between the number of neighboring ½m water holes and Rtþ1 was inconsistent. For instance, ½H there was a positive relationship for Rtþ1 , but not for ½L ½U Rtþ1 and Rtþ1 (Table 2, Fig. 3). In addition, when looking at the derived parameters, we found no relationship between the number of neighboring water holes and transition probabilities from low to high ½LH abundance (/t ; Fig. 4a). Under our a priori hypoth-

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esis that elephants tend to concentrate preferentially in areas with higher densities of water holes, we would have expected a positive relationship. An a posteriori hypothesis for the observed patterns is related to the competition for food resources, which should push elephants to avoid areas with high abundance of elephants. When the surface water is low elephants have no choice but to concentrate in areas with high water hole densities, but as the number of suitable water holes increases (with rainfall), elephants may disperse into less utilized areas, exploiting increased food production. This again might explain the lack of relationship between the number of neighboring water holes and ½LH /t (Fig. 4a) and the stronger negative relationship between the number of neighboring water holes and ½HL when precipitation is high (Fig. 4b). This a /t posteriori hypothesis is also supported by the fact that there was a negative relationship between rainfall and ½U ½L ½H Rtþ1 , Rtþ1 , and Rtþ1 (bˆ RAIN was negative; Table 2), which would indicate that as precipitation increases, elephants tend to disperse. Finally, models that included a ‘‘before vs. after 1996’’ effect were supported by the data and ½m indicated that transition probabilities Rtþ1 increased during the second half of the study period. In addition to being a valuable tool for investigating the spatiotemporal dynamics of animal populations, the type of model presented here can be used to parameterize management models or simulate how changes in environmental conditions may affect the distribution of elephants in the park. For instance, the dynamic model underlying our estimation is a Markov chain model (see also Martin et al. 2009a) of the type ntþ1 ¼ Hnt

ð3Þ

where nt is a column vector, 2 U3 nt 4 nL 5 t nH t that specifies the number of sites in each state at time t. For instance, nU t corresponds to the number of sites in state U, and H is a transition matrix that includes the transition probabilities among states U, L, and H: 3 2 UU /LU /HU /t t t 7 6 H ¼ 4 /UL /LL /HL t t t 5: /UH t

/LH t

/HH t

Estimates of some of these probabilities are presented in Fig. 4 and can be derived from estimates presented in Table 2 (by using Eq. 1). Based on Eq. 3, it would be possible to project the consequences of future changes in rainfall patterns (e.g., associated with global climate change) on elephant distribution and abundance categories in the park. However, we believe that this approach may be most useful in the context of structured decision making (e.g., Williams et al. 2002, Martin et al. 2009b). For instance, the managers’

FIG. 2. Relationships between annual rainfall and transi½m ½m tion probabilities (wtþ1 ), where wtþ1 is the probability of a water hole being suitable in year t þ 1, given that it was in state m in year t (with m ¼ U [unsuitable], L [suitable with low abundance of elephants], or H [suitable with high abundance]). The thick black lines correspond to the estimates of transition probabilities, and the thin black lines correspond to the 95% CI.

objective may be to achieve distribution and abundance categories of elephants that appear compatible with the socioeconomic and ecological needs of the park (e.g., that could be based on historical levels). In this case, the next step would be to develop a management model that links management actions to elephant distribution and abundance category. One potential action, in this specific case study, is to activate or deactivate artificial water pumps at water holes equipped with such devices. Once a management model has been developed, optimization methods such as stochastic dynamic programming (Lubow 1999, 2001) or reinforcement

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probably be considered when developing the management models. In any cases, our statistical analyses provide baseline estimates to parameterize such management models. It is also worth noting that one can think of several similar management problems. For example, for amphibians that breed in vernal pools, habitat (i.e., the vernal pool) may be considered as unsuitable if it is dry (MacKenzie et al. 2006); the management goal could then be to maintain a desired number of vernal pools occupied by amphibians while minimizing the cost associated with vernal pool management (e.g., mechanically manipulating pool size or depth; D. I. MacKenzie, J. D. Nichols, L. L. Bailey, and J. E. Hines, unpublished manuscript). Ideally, one should account for detection probabilities when estimating transition probabilities among occupancy or abundance states (Yoccoz et al. 2001, Williams et al. 2002). Unfortunately, the design of many historical

FIG. 3. Relationships between annual rainfall, the number of neighboring water holes (‘‘neighbors’’), and transition ½m ½m probabilities (Rtþ1 ). Rtþ1 is the probability of the water hole being in state H in year t þ 1 given that it is suitable in t þ 1 and was in state m in year t. The gray surface corresponds to the pre-1996 period, and the white surface to the post-1996 period.

learning (Fonnesbeck 2005) can then be applied to identify optimal decisions relative to specified objectives (e.g., Martin et al. 2009b). In our application, we believe that switching pumps on or off is more likely to lead to a behavioral response (i.e., movement) than a numerical response (i.e., mortality). However, these issues should

FIG. 4. Relationships between annual rainfall (mm), the number of neighboring water holes, and transition probabilities (/). Transition probabilities are between suitable sites (with high [H] and low [L] abundance of elephants). The gray surface corresponds to the pre-1996 period, and the white surface to the post-1996 period.

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PLATE 1. Elephant water hole survey from an observation platform. Photo credit: S. Chamaille´-Jammes.

large-scale monitoring programs does not allow for the estimation of detectability. In these instances the types of models presented here can be helpful to reduce errors associated with detectability by assigning individuals to broad classes of abundances instead of modeling uncorrected count data directly. Assigning observations to broad categories reduces the possibility of a misclassification error, which is a manifestation of imperfect detection (e.g., false absences). However, we agree with Yoccoz et al. (2001) and strongly encourage biologists to design monitoring programs that will explicitly consider both detection and sampling variation to avoid errors associated with these two sources of variations (otherwise, if detection probability is less than 1, resulting inference might be unreliable). In fact, in situations where repeated observations of each site have been conducted within a relatively short time frame each year, it is then possible to simultaneously estimate detection probabilities and transition probabilities with dynamic multistate site occupancy models (MacKenzie et al. 2009; D. I. MacKenzie, J. D. Nichols, L. L. Bailey, and J. E. Hines, unpublished manuscript). This is made particularly easy with the recent implementation of this model into the user-friendly software PRESENCE 2.2. To conclude, we see several advantages of our approach in wildlife habitat management and other ecological applications. First, the type of joint habitat– occupancy models that we applied provides a coherent

framework to examine how habitat suitability (and factors that affect habitat suitability) influences the distribution and abundance of organisms. Because of their simplicity, these models can also be used to apply structured decision-making tools in order to derive decisions that are optimal relative to specified objectives (e.g., Martin et al. 2009b). Indeed, this use was a motivation for this work. If detection probabilities cannot be estimated from existing data sets, pooling counts into large categories of abundance may be a reasonable approach to minimize state misclassification. Then, when better designs are implemented in order to collect the information needed to deal directly with detection probabilities, the same models can readily be framed to deal with such data (e.g., MacKenzie et al. 2009). In fact this similarity of models that do or do not make assumptions about perfect detection probability emphasizes a point that is not well understood by population index proponents. If one does have the fortunate situation in which detection probabilities are not an important issue (e.g., perhaps elephants in open landscapes), detection parameters may simply be constrained to equal 1 in the same software (e.g., PRESENCE) that has been developed to incorporate possible nondetection. This software still fits dynamic models and still presents parameter estimates and associated variance estimates that deal with estimation

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of multinomial parameters from samples of sites or individual animals. The central point is that claims of perfect detection do not absolve one from consideration of the other components of variation in dynamic modeling and estimation, and indeed such components are dealt with in the same software used to deal with the more general problems that include nondetection. Thus, the modeling framework presented in this paper should be applicable to a wide range of existing data sets, and should help to address important ecological, conservation, and management problems that deal with occupancy, abundance, and habitat suitability. ACKNOWLEDGMENTS This work was partially funded by the CNRS program ‘‘Ingeńierie Ećologique’’ and the BioFUN grant of the French ‘‘Agence Nationale de la Recherche’’ (ANR-05-BDIV-013-01). We are indebted to Wildlife Environment Zimbabwe, which provided the census data. LITERATURE CITED Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. Pages 267–281 in B. Petrov and F. Cazalo, editors. Proceedings of the Second International Symposium on Information Theory, Akademiai Kiado, Budapest, Hungary. Blanc, J. J., R. F. W. Barnes, G. C. Craig, H. T. Dublin, C. R. Thouless, I. Douglas-Hamilton, and J. A. Hart. 2007. African elephant status report. An update from the African elephant database. Occasional Paper of the IUCN Species Survival Commission, Number 33. Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference: a practical information-theoretic approach. Second edition. Springer-Verlag, New York, New York, USA. Chamaille´-Jammes, S., H. Fritz, and F. Murindagomo. 2007a. Climate-driven fluctuations in surface-water and the buffering role of artificial pumping in an African savanna: potential implications for herbivore dynamics. Austral Ecology 32: 740–748. Chamaille´-Jammes, S., H. Fritz, M. Valeix, F. Murindagomo, and J. Clobert. 2008. Resource variability aggregation and direct density dependence in an open context: the local regulation of an African elephant population. Journal of Animal Ecology 77:135–144. Chamaille´-Jammes, S., M. Valeix, and H. Fritz. 2007b. Managing heterogeneity in elephant distribution: interactions between elephant population density and surface-water availability. Journal of Applied Ecology 44:625–633. Chamaille´-Jammes, S., M. Valeix, and H. Fritz. 2007c. Elephant management: why can’t we throw out the babies with the artificial bathwater? Diversity and Distributions 13: 663–665. Clark, C. W., and M. Mangel. 2001. Dynamic state variable models in ecology. Oxford University Press, New York, New York, USA. Conroy, M. J., and C. T. Moore. 2001. Simulation models and optimal decision making in natural resource management. Pages 91–104 in T. M. Shenk and A. B. Franklin, editors. Modeling in natural resource management: valid develop-


ment, interpretation and application. Island Press, Washington, D.C., USA. Fonnesbeck, C. J. 2005. Solving dynamic wildlife resource optimization problems using reinforcement learning. Natural Resource Modeling 18:1–39. Hines, J. E. 2008. Program PRESENCE 2.2. USGS-PWRC. hhttp://www.mbr-pwrc.usgs.gov/software/presence.htmli Lande, R. 1987. Extinction thresholds in demographic models of territorial populations. American Naturalist 130:624–635. Lubow, B. C. 1999. Adaptive stochastic dynamic programming (ASDP). Supplement to SDP user’s guide. Version 2.2. Colorado State University, Fort Collins, Colorado, USA. Lubow, B. C. 2001. Adaptive stochastic dynamic programming (ASDP): Version 3.2. Colorado State University, Fort Collins, Colorado, USA. MacKenzie, D. I., J. D. Nichols, J. A. Royle, K. H. Pollock, J. E. Hines, and L. L. Bailey. 2006. Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Elsevier, San Diego, California, USA. MacKenzie, D. I., J. D. Nichols, M. E. Seamans, and R. J. Gutie´rrez. 2009. Modeling species occurrence dynamics with multiple states and imperfect detection. Ecology 90:823–835. Martin, J., C. L. McIntyre, J. E. Hines, J. D. Nichols, J. A. Schmutz, and M. C. MacCluskie. 2009a. Dynamic multistate site occupancy models to evaluate hypotheses relevant to conservation of Golden Eagles in Denali National Park, Alaska. Biological Conservation 142:2726–2731. Martin, J., M. C. Runge, J. D. Nichols, B. C. Lubow, and W. L. Kendall. 2009b. Structured decision making as a conceptual framework to identify thresholds for conservation and management. Ecological Applications 19:1079–1090. Nichols, J. D. 2001. Using models in the conduct of science and management of natural resources. Pages 11–34 in T. M. Shenk and A. B. Franklin, editors. Modeling in natural resource management: development, interpretation and application. Island Press, Washington, D.C., USA. O’Connor, T. G., P. S. Goodman, and B. Clegg. 2007. A functional hypothesis of the threat of local extirpation of woody plant species by elephant in Africa. Biological Conservation 136:329–345. Ovaskainen, O., and I. Hanski. 2003. Extinction threshold in metapopulation models. Annales Zoologici Fennici 40:81–97. Owen-Smith, N., G. I. H. Kerley, B. Page, R. Slotow, and R. J. Van Aarde. 2006. A scientific perspective on the management of elephants in the Kruger National Park and elsewhere. South African Journal of Science 102:389–394. Smit, I. P. J., C. C. Grant, and I. J. Whyte. 2007. Elephants and water provision: what are the management links? Diversity and Distributions 13:666–669. Stokke, S., and J. T. du Toit. 2002. Sexual segregation in habitat use by elephants in Chobe National Park, Botswana. African Journal of Ecology 40:360–371. Valeix, M., H. Fritz, S. Chamaille´-Jammes, M. Bourgarel, and F. Murindagomo. 2008. Fluctuations in abundance of large herbivore populations: insights into the influence of dry season rainfall and elephant numbers from long-term data. Animal Conservation 11:391–400. Williams, B. K., J. D. Nichols, and M. J. Conroy. 2002. Analysis and management of animal populations. Academic Press, San Diego, California, USA. Yoccoz, N. G., J. D. Nichols, and T. Boulinier. 2001. Monitoring of biological diversity in space and time. Trends in Ecology and Evolution 16:446–453.